I am working with very small cell counts, and am wondering if Fisher's exact test can be used in place of the chi-squared test when partitioning IxJ tables. I am interested if the same process for partitioning the tables is acceptable.
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You seem to be asking two questions:
Can Fisher's exact test be used for ixj tables?
Something about partitioning tables.
The answer to 1 is easy: Yes it can. In SAS there is an EXACT statement in PROC FREQ. In R there is fisher.test in the stats package.
The answer to 2 is unclear; you can certainly partition tables and test on the subsetted partition. If you test many partitions you run into all the multiple testing issues. If you choose your partition based on anything related to Fisher's test, then its properties will be off.
answered Apr 12, 2013 at 21:25
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$\begingroup$ Okay. My wording was poor. I was just wondering if I get a significant result from Fisher's exact test, can I then proceed to partition my table as I would were I using the chi square test. $\endgroup$ Commented Apr 12, 2013 at 22:08
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$\begingroup$ Yes, you can. The problems are the same whether you use chi-square or Fisher $\endgroup$ Commented Apr 12, 2013 at 22:13
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1$\begingroup$ user27008 Just a caveat - you can't choose which of Fisher or chi-square to use based on which one is most significant. Pick one kind of analysis both for the whole table and any partitions (where the choice is based on considerations other than the values within the table -- though basing that choice on the margins shouldn't matter). $\endgroup$– Glen_bCommented Jul 23, 2013 at 0:16